Dynamics of a class of Chua’s oscillator with a smooth periodic nonlinearity: Occurrence of infinitely many attractors

Abstract

In this article, a class of Chua’s system with smooth periodic nonlinear term is considered. This kind of systems exhibits strange dynamical behavior. Except for the existence of infinitely many equilibrium points, period-doubling bifurcation, and double-scroll attractors, this type of systems has strange dynamics different from the classical Chua’s system: (i) the coexistence of (infinitely) many non-chaotic strange attractors; (ii) the coexistence of (infinitely) many spiral chaotic attractors; (iii) the coexistence of multi-scroll attractors; (iv) “growing”-scroll attractors, where the number of scrolls is an increasing function with respect to the time variable.